Best route--Branson to Memphis?

A few mile further but I think faster than 62 across ARK. You can take 62 to 65 then north to 60 out of Springfield to 55 south. US 60 is a great road and lots of 4 lane.

Last time I was across 40 it was pretty rough IMHO.

I take 62-63-55-40 all the time. Less traffic, road has been redone most of the way and has been made into 4 lane for the majority of it. I travel it 2-3 times a year. 40 is rough and the expansion joints get very tiring quickly.

That is the way I would go. There are shorter ways but it will take longer. 62 to 63 is a PITA until you get to Jonesboro.